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Step 1
Sift together flour, baking powder, and salt in a large bowl.
Step 2
Using an electric mixer, beat butter until light and fluffy, about 3 minutes. Add in sugar and beat an additional 2 minutes more. Add eggs, one at a time, beating after each addition, followed by the vanilla. Add the flour mixture and beat on low until just combined.
Step 3
Divide the dough in half. Form half of the dough into a 4 by 4-inch square, wrap in plastic wrap, and set aside. Return the other half of the dough to the mixing bowl. Using a double boiler or a microwave on low power, melt the chocolate, stirring until smooth. Mix the melted chocolate into the dough just until combined. Form the chocolate dough into a 4 by 4-inch square, wrap in plastic wrap, and place both chocolate and vanilla doughs into the refrigerator for 30 minutes (or up to 3 days).
Step 4
Cut each dough into four even strips. Roll out one strip of vanilla dough between two sheets of parchment paper, into a roughly 6-by-7 inch rectangle. Repeat with a strip of the chocolate dough. Peel off the top sheet of parchment paper from each dough and flip the vanilla dough over onto the chocolate dough. Trim excess dough into a rectangle and run a rolling pin lightly over the dough to ensure they stick together. Peel off the top sheet of parchment paper, then roll the dough into a log. Wrap in plastic wrap and refrigerate. Repeat with remaining strips of dough to form 4 logs.
Step 5
Refrigerate logs for 1 hour, then remove from refrigerator and roll each log on the counter several times to prevent the bottom from flattening. Transfer to the freezer for 2 hours, or up to 3 months. Keep dough frozen until ready to slice and bake.
Step 6
Preheat oven to 350 °F and line a baking sheet with parchment paper. Using a sharp knife, slice dough into 1/4-inch thick slices and place 1 1/2 inches apart on the prepared baking sheet. Bake until vanilla dough is slightly golden, 9 to 11 minutes. Cool cookies on a wire rack.